AMM Liquidity Providers Can Trail a Hold Strategy as Prices Shift

An automated market maker position can rise in dollar value and still leave a liquidity provider behind a hold strategy, because changing token prices alter what the pool owns.

Impermanent loss describes the difference between an automated market maker (AMM) liquidity position and the value of keeping the same starting assets. It is a comparison at a given point in time, not a standalone measure of whether the position made money. A pool position can be worth more than the original deposit and still be worth less than holding those original assets.

In a constant-product AMM, traders swap directly against a token pool. The pool follows the relationship x × y = k, where x and y represent the amounts of the two tokens and k remains constant under the model. As trades change the pool’s balance, its mix shifts. If Ether (ETH) rises against USD Coin (USDC), the pool ends up with less ETH and more USDC. The liquidity provider’s position changes with that mix.

How the comparison works

For a fee-free, 50/50 constant-product pool, the relative difference from holding is 2√r / (1 + r) - 1. Here, r is the new relative price of the two assets divided by their starting relative price. Multiply the result by 100 to express it as a percentage. A negative result means the pool position trails the hold comparison.

The formula describes one specific setup. It does not cover every AMM design, and it leaves out swap fees, rewards and other costs. It also does not by itself show the net result for a concentrated-liquidity position, whose behavior depends on its selected price range.

Consider a hypothetical deposit of one ETH, priced at $2,000, and 2,000 USDC. The starting portfolio is worth $4,000. If ETH doubles to $4,000, holding the original assets would produce a $6,000 portfolio: $4,000 in ETH and $2,000 in USDC.

Under the simplified pool model, the position would instead contain about 0.7071 ETH and 2,828.43 USDC. At the new ETH price, those balances would be worth about $5,656.85. That is $343.15 less than the hold value, a gap of about 5.72%. The pool position has gained about $1,656.85 from its starting value, but holding the original assets would have gained $2,000.

The example depends on its starting mix and the assumed price change. It is not a forecast or a measure of what a particular pool will return. The comparison uses the value of the original token amounts at the new prices, rather than comparing the pool only with its initial deposit.

A decline in the relative price can also produce a gap between the pool and holding. In the simplified model, that gap returns to zero if the relative price returns to its starting point while the position remains in the pool. The word “impermanent” does not mean the difference will necessarily reverse: if a provider exits while prices have diverged, the withdrawn token mix reflects the prices at that time.

Concentrated liquidity changes the trade-off

Uniswap v3 and v4 let liquidity providers choose the price interval in which their capital is active. A position within its chosen range can earn swap fees on trades while its liquidity is active. If the market price moves outside the interval, the position becomes inactive, stops earning new swap fees and consists of one token. It can become active again if the price returns to the range.

Fee income depends in part on how much active liquidity a provider contributes and whether the selected range continues to include the market price. A narrower range concentrates capital in a chosen interval, but the position’s activity and fee income depend on where the market price moves. The fee-free, full-range formula cannot capture those range-specific results.

What the comparison leaves out

A displayed annual percentage rate (APR) does not show how a liquidity position performed against holding the original assets. A fuller comparison considers the position’s current value, collected fees and rewards, and the costs of managing or adjusting the position. Fees may offset some of the difference, but they are not guaranteed to do so.

The same distinction matters in yield farming, where trading fees and token rewards can sit alongside impermanent-loss risk. A pool balance can rise in dollar terms while its changing token mix trails the original holdings. The result depends on the AMM design, relative price movement, selected range, fee income and costs; no single formula captures every liquidity provider’s net return.